Na, barely a day and you can sign it.
I can’t agree it isn’t complicated.
Ultimately it’s a seven platform London terminal feeding into two lines, via a reversible and an extremely steep curve, with a siding and a spur towards Charing Cross. There are a lot of traps: leaving on a single yellow and then SPADDing without an AWS warning; reading across and SPADDing the signals on the curve towards London Bridge, I can think of several examples of each over the past five years. Also an example of a serious gapping that crippled the throat for hours during the peak, not to mention the risk of being wrong routed towards Charing Cross from certain platforms. It’s not the hardest terminal station I’ve ever signed, but it’s certainly not the easiest.
In terms of GTR signing it as an occasional diversion, that might have been doable when many of their Kent services were driven by SE metro drivers who signed CST anyway. That was now years ago and it’s a huge knowledge requirement to bring in for GTR drivers who nowadays (AIUI) literally sign just LB and the route to and from the core.
Even if it could be learned in a day - which I would dispute - that would mean sending people from as far afield as Cambridge, Peterborough, Brighton etc. to stand around on LB asking to be let into cabs of networkers, or else watching the usual dreadful (and often wrong) track access videos.
Could it be done? Of course, but I’d question what possible purpose it would serve, which brings us neatly onto…
It's not a solution looking for a problem though, as the current "solution" is cancelling the Rainham TL service completely, even if south of the river there are no issues at all.
As others have pointed out, usually you end up with Rainham Shuttles to and from London Bridge then a simple interchange which, when the core is closed, most weekend leisure travellers will be making anyway. Far more will want the west end, or to continue their journey via the tube, than will want to go to Cannon St, or to Blackfriars for that matter. Both have limited onward connections and, almost uniquely in London, the areas around them remain (relatively) ghost-town like at weekends.
Even if you’ve got no GTR Rainham services along the north Kent line, depending where on the route you live, you’ve got plenty of options: DLR, Crossrail (soon), SE go from Dartford to London four ways. Passengers for London from Medway can take an SE mainliner to Victoria via the Chathams. That’s usually a lot quicker and more pleasant than GTR’s crawl via the north Kent!